As social animals, primates need to cooperate with each other to reap the benefits of living in a group. Individuals within a group, however, have competing interests as they fight over resources. We used a competitive game to investigate decision-making in a situation in which it pays to be unpredictable (to avoid exploitation) but to be able to predict another’s moves (to gain an advantage). Twelve capuchins, four rhesus monkeys, and 80 humans played in pairs against each other by each choosing between two options on a computer screen. One player was rewarded when both selected the same target, whereas the other player was rewarded when they chose opposite targets. Both humans and monkeys met game-theoretic predictions in the symmetric game, in which players should select between the two options randomly in order to maximize gain (no deviation from predictions; humans: chi-square(1) = 1.03, p = .311, monkeys: chi-square(1) = 1.34, p = .248). However, the asymmetric game required one of the players to choose between options at a 25:75 ratio. Monkeys adjusted their strategies in the expected directions (chi-square(1) = 0.11, p = .740), whereas humans again played 50:50 (deviating significantly from equilibrium predictions: chi-square(1) = 80.06, p < .001). These results suggest that, in a competitive context, humans may favor acting unpredictably to win a given round over maximizing overall gain.